PSI: Exact Symbolic Inference for Probabilistic Programs

Conference paper

DOI: 10.1007/978-3-319-41528-4_4

Volume 9779 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Gehr T., Misailovic S., Vechev M. (2016) PSI: Exact Symbolic Inference for Probabilistic Programs. In: Chaudhuri S., Farzan A. (eds) Computer Aided Verification. CAV 2016. Lecture Notes in Computer Science, vol 9779. Springer, Cham


Probabilistic inference is a key mechanism for reasoning about probabilistic programs. Since exact inference is theoretically expensive, most probabilistic inference systems today have adopted approximate inference techniques, which trade precision for better performance (but often without guarantees). As a result, while desirable for its ultimate precision, the practical effectiveness of exact inference for probabilistic programs is mostly unknown.

This paper presents PSI (, a novel symbolic analysis system for exact inference in probabilistic programs with both continuous and discrete random variables. PSI computes succinct symbolic representations of the joint posterior distribution represented by a given probabilistic program. PSI can compute answers to various posterior distribution, expectation and assertion queries using its own back-end for symbolic reasoning.

Our evaluation shows that PSI is more effective than existing exact inference approaches: (i) it successfully computed a precise result for more programs, and (ii) simplified expressions that existing computer algebra systems (e.g., Mathematica, Maple) fail to andle.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.ETH ZurichZurichSwitzerland
  2. 2.University of Illinois at Urbana-ChampaignChampaign and UrbanaUSA